Problem: Solve for $x$ and $y$ using substitution. ${-4x+5y = -7}$ ${y = 4x+5}$
Solution: Since $y$ has already been solved for, substitute $4x+5$ for $y$ in the first equation. ${-4x + 5}{(4x+5)}{= -7}$ Simplify and solve for $x$ $-4x+20x + 25 = -7$ $16x+25 = -7$ $16x+25{-25} = -7{-25}$ $16x = -32$ $\dfrac{16x}{{16}} = \dfrac{-32}{{16}}$ ${x = -2}$ Now that you know ${x = -2}$ , plug it back into $\thinspace {y = 4x+5}\thinspace$ to find $y$ ${y = 4}{(-2)}{ + 5}$ $y = -8 + 5$ $y = -3$ You can also plug ${x = -2}$ into $\thinspace {-4x+5y = -7}\thinspace$ and get the same answer for $y$ : ${-4}{(-2)}{ + 5y = -7}$ ${y = -3}$